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Application of Correspondence Analysis and Related Methods to Evaluation of Knowledge and Skills of Students prof. Jozef Dziechciarz dr Alicja Grzeskowiak dr Agnieszka Stanimir Education Policy Background Main goal of education reform

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SLIDE 1

Application of Correspondence Analysis and Related Methods to Evaluation of Knowledge and Skills

  • f Students
  • prof. Jozef Dziechciarz

dr Alicja Grzeskowiak dr Agnieszka Stanimir

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SLIDE 2

Education Policy Background

Main goal of education reform (Poland, 1999):

“the improvement of quality in formal educational system and its adjustment to requirement of the knowledge-base economy, assuring the access to lifelong learning system for the entire society”

Source: Perspektywy gospodarki opartej o wiedzę w Polsce; World Bank Report, KBN, 2004

Principles of the reform:

  • new structure of the education system, ranging from

nursery school to doctoral studies

  • an independent assessment, external examination

system

  • supervision separated from management
  • new system of financing
  • new professional status of the teaching staff linked

with the promotion paths

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 3

Education Reform and PISA (Programme for International Students Assessment) Surveys

  • 1999 – PISA trial version of survey, introduction of

Education Reform in Poland

  • 2000

– PISA first survey, participating Polish students approaching the end

  • f

compulsory education in the old system (very good baseline for comparisons)

  • 2009 – fourth PISA survey; after ten years after the

introduction of the reform Poland’s participation was summarized as:

„on average, the reform was associated with significant

  • improvements. Poland improved its score in mathematics

by 0.25 of a standard deviation, in reading, by 0.28 of a standard deviation, and in science, by 0.16 of a standard deviation”

Source: The Impact of the 1999 Education Reform in Poland, OECD Education Working Paper no.49, OECD, 2010 CARME Conference, Rennes, 8-11 February 2011

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SLIDE 4

Scope of Research

  • PISA results evaluation was published in

2009 but the newest information taken into consideration was from 2006

  • the need for evaluation based on the up-

to-date results

  • national

exam results from 2010 analyzed, similar competences as PISA test regarded

  • special

attention paid to differences according to gender, place of residence and to changes in time

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 5

Gymnasium as a Part of Education System in Poland

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Source: The Education and Assessment System in Poland ,Central Examination Board, 1999

Analyzed education level

  • Age of students:

14-16

  • General education
  • Compulsory school
  • No specialization

paths

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SLIDE 6

Source: Central Examination Board

Regional Aspect of the Study

CARME Conference, Rennes, 8-11 February 2011

8 Regional Examination Boards

  • south-western part of the country (two administrative territories)
  • area: 29 thousand km2 (9,1% of total)
  • population: 3,9 million (10,2% of total)
  • number of students taking the exam: 40,9 thousand (9,2% of total)
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SLIDE 7

External Exams Idea

Standardized Procedures Nationwide comparability of results Examination papers coded to provide

  • bjective assessment

Not relevant for graduation, relevant for further enrolment External Exams

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 8
  • Mathematics
  • Physics
  • Astronomy
  • Chemistry
  • Biology
  • Geography

Science

  • Polish language
  • History
  • Civic education
  • Arts

Humanities

Gymnasium Exam - Division

CARME Conference, Rennes, 8-11 February 2011

max 50 points max 50 points

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SLIDE 9
  • Finding and using information
  • Application of terms and

procedures

  • Identifying and describing

facts, relationships and dependences

  • Application of integrated

knowledge and skills to solve problems

Science

  • Reading and interpretation of

texts

  • Creation of own text

Humanities

Evaluated Competences Areas

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 10

General Remarks on Results (2010)

CARME Conference, Rennes, 8-11 February 2011 1 2 3 4 5 6 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

%

number of points

science humanities

Median 22 Median 31

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SLIDE 11

Population Structure (2010)

CARME Conference, Rennes, 8-11 February 2011

50,03% 49,97%

Gender

Female Male

21% 25% 35% 19%

Place of Residence by Commune Type

Urban (cities more than 80 th inhabitants) Urban (towns less than 80 th inhabitants) Urban-rural Rural

  • urban commune:

limited to the administrative town/city borders

  • rural commune:

the territory does not comprise a town

  • urban-rural:

includes a town and some villages

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SLIDE 12

Multivariate CA Based on Burt’s Matrix

  • results obtained in points were coded as

excellent, good, moderate and weak

  • two

analyses for two administrative territories (Lower Silesia Region and Opolskie Region) were conducted

  • quality of display in two-dimensional space

was equal to 26% and 30%, respectively (to regions)

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 13

URBAN RURAL URBAN/RURAL C.JG. C.LEG. WROCLAW GENDER:G GENDER:B HUM.:EXCELLENT HUM.:GOOD HUM.:MODERATE HUM.:WEAK SCIENCE:EXCELLENT SCIENCE:MODERATE SCIENCE:GOOD SCIENCE:WEAK

  • 2,0
  • 1,5
  • 1,0
  • 0,5

0,0 0,5 1,0 1,5 2,0 1=0,44 (14,78%)

  • 2,0
  • 1,5
  • 1,0
  • 0,5

0,0 0,5 1,0 1,5 2,0 2=0,24 (11,29%) URBAN RURAL URBAN/RURAL C.JG. C.LEG. WROCLAW GENDER:G GENDER:B HUM.:EXCELLENT HUM.:GOOD HUM.:MODERATE HUM.:WEAK SCIENCE:EXCELLENT SCIENCE:MODERATE SCIENCE:GOOD SCIENCE:WEAK URBAN RURAL URBAN/RURAL OPOLE GENDER:B GENDER:G HUM.:EXCELLENT HUM.:GOOD HUM.:MODERATE HUM.:WEAK SCIENCE:MODERATE SCIENCE:GOOD SCIENCE:EXCELLENT SCIENCE:WEAK

  • 2,0
  • 1,5
  • 1,0
  • 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1=0,42 (16,88%)

  • 2,0
  • 1,5
  • 1,0
  • 0,5

0,0 0,5 1,0 1,5 2,0 2,5 2=0,33 (13,31%) URBAN RURAL URBAN/RURAL OPOLE GENDER:B GENDER:G HUM.:EXCELLENT HUM.:GOOD HUM.:MODERATE HUM.:WEAK SCIENCE:MODERATE SCIENCE:GOOD SCIENCE:EXCELLENT SCIENCE:WEAK

Multivariate CA Based on Burt’s Matrix - Results

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Lower Silesia Region Opolskie Region

Excellent results in big cities Girls better results than boys in both science and humanities Weak results associated neither with gender nor with commune type

As the analysis based on Burt’s matrix did not indicated the exact diversification among the gymnasium students the data were analyzed with application

  • f

multiway contingency tables.

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SLIDE 14

Analysis Based on Multiway Contingency Tables

  • higher-order associations were applied

between commune type and gender and between knowledge area and exam score

  • data

table used in this analysis is 20x8, dimensionality of this table is 7

  • percentage of explained inertia in the

map is 96%

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 15

DS-U-B DS-U/R-B DS-R-B DS-JG-G DS-JG-B DS-LEG-G DS-LEG-B WROCLAW-G WROCLAW-B OP-U-B OP-U/R-B OP-U-B OP-OP-G OP-OP-B HUM.-GOOD HUM.-MODERATE HUM.-EXCELLENT HUM.-WEAK SCIENCE-GOOD SCIENCE-MODERATE SCIENCE-EXCELLENT SCIENCE-WEAK

  • 0,5
  • 0,4
  • 0,3
  • 0,2
  • 0,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 1=0,04 (75,16%)

  • 0,5
  • 0,4
  • 0,3
  • 0,2
  • 0,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 2=0,01 (20,40%) DS-U-B DS-U/R-B DS-R-B DS-JG-G DS-JG-B DS-LEG-G DS-LEG-B WROCLAW-G WROCLAW-B OP-U-B OP-U/R-B OP-U-B OP-OP-G OP-OP-B HUM.-GOOD HUM.-MODERATE HUM.-EXCELLENT HUM.-WEAK SCIENCE-GOOD SCIENCE-MODERATE SCIENCE-EXCELLENT SCIENCE-WEAK

Analysis Based on Multiway Contingency Tables – General Results

CARME Conference, Rennes, 8-11 February 2011

Boys from the capital of the region excellent in science Boys from other big cities good in science Girls from big cities excellent in humanities Boys from rural and urban-rural communes moderate in humanities No particular categories associated with weak results in humanities No particular categories associated with weak results in science

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SLIDE 16
  • 0,4
  • 0,3
  • 0,2
  • 0,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 1=0,03 (76,99%)

  • 0,4
  • 0,3
  • 0,2
  • 0,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 2=0,008 (19,21%)

BOYS GIRLS GIRLS BOYS Wrocław Big cities Urban Urban/rural Rural

  • S. - EXC.
  • H. - EXC.
  • H. - G
  • H. - M
  • H. - W
  • S. - G
  • S. - M
  • S. - W

Analysis Based on Multiway Contingency Tables: Lower Silesia Region – General Overview

CARME Conference, Rennes, 8-11 February 2011

Capital of the region Science Excellent Science Weak Humanities Weak Both Moderate Both Good Humanities Excellent

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SLIDE 17
  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 1=0,05 (69,88%)

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 2=0,052 (26,94%)

2003 2010

Wrocław Rural Wrocław Rural S.-EXC. H.-EXC H.-G H.-M H.-W S.-G S.-M S.-W

Comparison of Results Obtained in 2003 and 2010

CARME Conference, Rennes, 8-11 February 2011

From better results in the capital of the region to weaker results in rural communes From better results in the capital of the region to weaker results in rural communes Various changes in science results:

  • Cities: better results in 2010
  • Urban-rural communes: weaker results in 2010
  • Rural communes: weaker results in 2010

No particular differences in humanities results in 2003 and 2010

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SLIDE 18
  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 1=0,05 (60,43%)

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 2=0,02 (25,42%)

Wroclaw -girls Wroclaw -girls U/R, R -girls U/R, R -girls U/R, R -boys U/R, R -boys Wroclaw -boys Wroclaw -boys 2003 2010 S.-EXC. S.-G S.-M S.-W H.-EXC. H.-G H.-M H.-W

Comparison of Results Obtained in 2003 and 2010

CARME Conference, Rennes, 8-11 February 2011

Girls obtained better results than boys in both areas regardless of the place of residence Bigger dispersion of results according to gender was

  • bserved in rural and urban-

rural communes

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SLIDE 19

Other Methods: Application of Factor Analysis

  • problem – identification of common

factors in the competences areas

  • design - variants of analysis (issues):

students divided according to gender and place of residence; each issue analyzed separately

  • result
  • the

competences areas produce

  • ne

common factor in all variants

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 20

Further Research Directions

  • PISA

results from

  • ther

European countries

  • Exploring results in connection

with information from background questionnaires concerning:

educational carrier (educational aspirations, school changing, studying interruptions)

ICT familiarity (availability

  • f

ICT, attitude and use of computers)

parents characteristics (educational status, economical status, attitude to reading, perception of and involvement in child’s school, child’s school choice criteria)

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 21

Conclusions

  • the application of correspondence analysis to

the study of knowledge and skills of students allowed to identify the associations among analyzed characteristics (gender, commune type, competences areas, results of exam)

  • the application of the multiway contingency

table also allowed to identify the relationships in any configuration of variables as well as improves the quality of presentation in low dimensional space

  • there are further research directions as taking

into consideration results from more years or extending the study to other countries and

  • ther characteristics

CARME Conference, Rennes, 8-11 February 2011

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SLIDE 22

Thank you very much for your attention

CARME Conference, Rennes, 8-11 February 2011